[PS] More fixes

This commit is contained in:
2026-06-15 18:13:04 +02:00
parent 2828d5e0f0
commit 79aaaa687e
22 changed files with 44 additions and 39 deletions
@@ -1,12 +1,13 @@
\subsection{Stetige Zufallsvariablen}
\shortdefinition $\cX$ stetig $\E[\cX] = \int_{-\8}^{\8} x f_\cX(x) \dx x$
\shorttheorem $\E[\varphi(\cX)] = \int_{-\8}^{\8} \varphi(x) f_\cX(x) \dx x$, falls int. wohldefiniert
\shorttheorem $\E[\varphi(\cX)] = \int_{-\8}^{\8} \varphi(x) f_\cX(x) \dx x$, falls int. wohldef.
\shortlemma[Int über gauss. Glockenk.] $\int_{-\8}^{\8} e^{\frac{-x^2}{2\sigma^2}} \dx x = \sqrt{2 \pi \sigma^2}$
\subsubsection{Beispiele}
% TODO: Consider if need derivation of them here and prev section as well
% TODO: Also add the ones proven in exercises
\shortlemma[Int über gauss. Glockenk.] $\int_{-\8}^{\8} e^{\frac{-x^2}{2\sigma^2}} \dx x = \sqrt{2 \pi \sigma^2}$
\begin{itemize}
\item $\cX \sim \cU([a, b])$, $a < b$: $\E[\cX] = \frac{a + b}{2}$
\item $\cX \sim \text{Exp}(\lambda)$, $\lambda > 0$: $\E[\cX] = \frac{1}{\lambda}$